Postwar Germany has witnessed at least two trials of monumental historical significance: the 1963 Frankfurt trial against Nazis who organised and ran Auschwitz concentration camp, and the 1975 trial of leading figures in the Baader-Meinhof group, of which I was briefly a member.

Now there may be a third: Munich this week saw the start of the trial against Beate Zschäpe, a former member of a neo-Nazi terrorist group called the National Socialist Underground. Zschäpe is accused of complicity in 10 cases of murder between 2000 and 2007, mainly of citizens of Turkish descent. Turkish newspapers have described it as Germany's new "trial of the century".

It is not just details of the crimes that are shocking, but the fact that it has taken 13 years to bring the first murder to court, with investigators originally suspecting the victims' families. The whole episode seemed to show that institutional racism is still a much bigger problem in Germany than the authorities like to admit, and that the country is urgently in need of the kind of reforms that Britain saw in the wake of the death of Stephen Lawrence. Were the police just incompetent, or "blind in the right eye"? A placard at a demonstration outside the courtroom on Monday asked the same question in simpler and more urgent terms: "How could they kill so many?"

Yet it is crucial to remember that the answer won't be found at the high-profile Zschäpe trial, but in an investigation already under way into police conduct. Three senior officers from the domestic intelligence agency – have already lost their jobs. The Green party and leftwing Die Linke are furthermore calling for a ban on recruiting police informers from far-right circles. Recently many have criticised the authorities for failing to recognise that the trial against Zschäpe will fulfil a similarly political role: seats for the media were originally assigned on a first-come first-served basis, which meant Turkish and Greek newspapers were left out. The federal court intervened, seats were reassigned – to the effect that major TV outlets and newspapers were left out at the expense of local radio stations and a women's magazine. Add to the farcical tone of the proceedings, the defence team carries the surnames Sturm, Stahl and Heer (Storm, Steel and Army). But the courts insist that everything must be done to stop this becoming a show trial – and I believe they are right.

In many ways the judiciary's desire to scale back the trial is the logical conclusion of Germany's negative experience of the Baader-Meinhof trial, where paranoia was so ripe that a separate courtroom was built next to Stammheim prison and many felt that the trial became a stage for political propaganda.

This time the danger is not so much that the far-right could hijack the trial for their own means, but that the media will start to dictate and orchestrate proceedings: at worst, they will build up expectations that a trial of this kind can never fulfil. Above everything, the trial should be about proving Zschäpe's involvement in the murders: concrete proof is still missing.

I am cautious of drawing parallels between this trial and the one that shaped my generation. But one parallel seems relevant: the NSU trio all grew up in East Germany (Zschäpe was born in 1975, Uwe Mundlos in 1973 and Uwe Böhnhardt in 1977) , which is to say a state – the GDR – in which anti-fascism was often dictated from the top down. Ordinary citizens were given little chance to work through their historical inheritance themselves.

All three NSU members were radicalised around the time of the fall of the Berlin Wall, as the old order collapsed. In this ensuing vacuum, with the western media quick to brand anyone from the east as a former Stasi member, many from the former GDR felt left behind. The ideologies and costumes of National Socialism became attractive to them precisely because their parents had kept quiet about that episode in German history – an equivalent of the protest movement that West Germany saw in the 1970s, just on the other extreme.

I don't believe that modern Germany is full of Nazis or neo-Nazis – like most Germans, I believe it is predominantly a cosmopolitan, enlightened place. If we want the world to show that this is true, we need to guarantee that Zschäpe is given a fair trial. My generation fluffed the chance to deal with its own traumas properly – I hope this one gets it right.